List questions from homological-algebra

Published on 28 Mar 2026 - 17:57

124

Views

When $\textrm{Tor}_n^A(-,A/radA)\neq 0$? ($A$ a finite dimensional $K$-algebra)

Published on 25 Mar 2026 - 6:03

63

Views

$f$ is a cycle since it is a loop, and since $H_1(point) = 0$, $f$ must then be a boundary.

Published on 01 Jun 2019 - 23:31

269

Views

$\mathbb{Z}$ has cohomological dimension one

Published on 03 Jun 2019 - 20:53

64

Views

Why does $H_{n}(\operatorname{Hom}_{R}(M,I_{\ast}(N))=H_{n}(\operatorname{Hom}_{R}(P_{\ast}(M),N))$?

Published on 26 Mar 2026 - 3:13

456

Views

Serre classes and the Serre spectral sequence

Published on 25 Mar 2026 - 9:22

291

Views

Cute/striking application(s) of Snake Lemma outside homological algebra

Published on 25 Mar 2026 - 4:40

552

Views

Prime ideals and maximal ideals of the Pullback of rings

Published on 23 Feb 2026 - 3:00

52

Views

Finite representation-infinite rings

Published on 08 Jun 2019 - 19:10

149

Views

Why do we want to compute derived functors via forgetful functors though easier?

Published on 25 Mar 2026 - 7:49

78

Views

Show that any monomorphism and a homomorphism can be embedded into a commutative diagram with exact rows.

Published on 26 Mar 2026 - 1:34

232

Views

Prove $F[x]/(x^n)$ is an injective module

Published on 25 Mar 2026 - 12:48

529

Views

Extending maps from a submodule

Published on 09 Jun 2019 - 19:19

127

Views

group homomorphism $\Phi: \pi_1(X,x_0)^{ab}\to H_1(X,\mathbb{Z})$ where $\pi_1(X,x_0)^{ab}$ is the abelianization of the group $\pi_1(X,x_0)$.

Published on 09 Jun 2019 - 21:47

84

Views

Functor $L:\mathcal{A}\to\mathcal{B}$ is left adjoint to $R$ functor, then $L$ preserves all colimit.

Published on 25 Mar 2026 - 9:50

List Question

Quotient of category of f.g. modules by subcategory

When $\textrm{Tor}_n^A(-,A/radA)\neq 0$? ($A$ a finite dimensional $K$-algebra)

$f$ is a cycle since it is a loop, and since $H_1(point) = 0$, $f$ must then be a boundary.

$\mathbb{Z}$ has cohomological dimension one

Why does $H_{n}(\operatorname{Hom}_{R}(M,I_{\ast}(N))=H_{n}(\operatorname{Hom}_{R}(P_{\ast}(M),N))$?

Serre classes and the Serre spectral sequence

Cute/striking application(s) of Snake Lemma outside homological algebra

Prime ideals and maximal ideals of the Pullback of rings

Finite representation-infinite rings

Why do we want to compute derived functors via forgetful functors though easier?

Show that any monomorphism and a homomorphism can be embedded into a commutative diagram with exact rows.

Prove $F[x]/(x^n)$ is an injective module

Extending maps from a submodule

group homomorphism $\Phi: \pi_1(X,x_0)^{ab}\to H_1(X,\mathbb{Z})$ where $\pi_1(X,x_0)^{ab}$ is the abelianization of the group $\pi_1(X,x_0)$.

Functor $L:\mathcal{A}\to\mathcal{B}$ is left adjoint to $R$ functor, then $L$ preserves all colimit.

Trending Questions

Popular # Hahtags

Popular Questions